Spherulite growth kinetics

To investigate the morphology and crystal growth in PLLA, atomic force microseopy (AFM) ean also be used. This teehnique can produce high-quality images and more aeeurate measurements than PLOM, although it is usually only restrieted to the sample surface.  

Regime transition is presented when the data are analyzed with the Lauritzen and Hoffman kinetic theory. Di Lorenzo demonstrated that the discontinuity in the spherulite growth rate is not associated to any change in superstructural morphology. Tsuji et al. and Yuryev et al. also observed this unusual bimodal crystallization behaviour for pure PLLA, while the normal characteristic bell-shaped spherulite growth rate dependence was seen for poly(L/D-lactide) copolymers. 

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The effect on spherulite growth kinetics of introducing HV comonomer units into the HB chain has not been quantitatively studied to date, although it is clear that the crystallization rate is reduced by increasing the HV content. Similarly the nucleation processes in HB-HV copolymers have not been extensively examined but these polymers do appear to be nucleated by the same materials that are effective in PHB. 

It has been reported that the overall rate of crystallization of pure PHB is relatively low compared to that of common synthetic polymers, showing a maximum in the temperature range of 55-60°C [23]. The spherulite growth rate kinetics have been evaluated [59] in terms of the theory by Hoffmann et al. [63], At about 90 °C, the spherulite growth rate displayed a maximum, which is not excessively low compared to that of common synthetic polymers. Therefore it was stated that the low overall crystallization rate of PHB centers on the nuclea-tion process rather than the subsequent crystal growth. Indeed, it has been shown that PHB has an exceptionally low level of heterogeneous nuclei [18]. 

Fig. 8 a Spherulitic growth rates for PPDX and the PPDX block within D7732C2310 diblock copolymer. Solid lines are fits to Lauritzen and Hoffman theory, b Lauritzen and Hoffman kinetics theory plot for PPDX (K = 17.2 x 104 K2) and the PPDX block within D7732C2310 diblock copolymer (K = 46 x 104 K2). (From [103]. Reproduced with permission of the Royal Society of Chemistry)... 

The isothermal crystallization of PEO in a PEO-PMMA diblock was monitored by observation of the increase in radius of spherulites or the enthalpy of fusion as a function of time by Richardson etal. (1995). Comparative experiments were also made on blends of the two homopolymers. The block copolymer was observed to have a lower melting point and lower spherulitic growth rate compared to the blend with the same composition. The growth rates extracted from optical microscopy were interpreted in terms of the kinetic nucleation theory of Hoffman and co-workers (Hoffman and Miller 1989 Lauritzen and Hoffman 1960) (Section 5.3.3). The fold surface free energy obtained using this model (ere 2.5-3 kJ mol"1) was close to that obtained for PEO/PPO copolymers by Booth and co-workers (Ashman and Booth 1975 Ashman et al. 1975) using the Flory-Vrij theory. 

Wu and Woo [26] compared the isothermal kinetics of sPS/aPS or sPS/PPE melt crystallized blends (T x = 320°C, tmax = 5 min, Tcj = 238-252°C) with those of neat sPS. Crystallization enthalpies, measured by DSC and fitted to the Avrami equation, provided the kinetic rate constant k and the exponent n. The n value found in pure sPS (2.8) points to a homogeneous nucleation and a three-dimensional pattern of the spherulite growth. In sPS/aPS (75 25 wt%) n is similar (2.7), but it decreases with increase in sPS content, whereas in sPS/PPE n is much lower (2.2) and independent of composition. As the shape of spherul-ites does not change with composition, the decrease in n suggests that the addition of aPS or PPE to sPS makes the nucleation mechanism of the latter more heterogeneous. 

Figure 10.9 shows the kinetics of spherulite growth in polypropylene containing different amounts of CaCOs. Polypropylene with no filler grew spherulites of a large size over a long period of time. The addition of CaCO reduced the ultimate size of the spherulite and also shortened the time to reach an equilibrium size. ... 

Figure 10.10 illustrates the kinetics of spherulite formation with and without fillers. The left half of each photograph shows spherulite growth without a filler. Two attributes of this growth are evident ... 

The process of formation of the crystalline state is controlled by the kinetics of nucleation and this may arise in a number of ways. Primary nucleation in a quiescent state must be associated with foreign bodies such as deliberately added nucleating agents, such as fine talc particles, or residual impurities such as heterogeneous catalyst particles followed by spherulite growth. The plot of extent of crystallinity, (p, as a function of time is sigmoidal in nature and follows an Avrami equation of the form... 

The discussion on the crystallization behavior of neat polymers would be expected to be applicable to immiscible polymer blends, where the crystallization takes place within domains of nearly neat component, largely unaffected by the presence of other polymers. However, although both phases are physically separated, they can exert a profound influence on each other. The presence of the second component can disturb the normal crystallization process, thus influencing crystallization kinetics, spherulite growth rate, semicrystalline morphology, etc. 

Temperature Dependence of the Spherulite Growth Rate and the Overall Kinetic Rate Constant... 

The presence of HOCP considerably slows down the melt crystallization process of PB-1. Therefore, the adopted values, lowered by increasing the HOCP fraction, provided similar rates of crystallization for pure PB-1 and blends. Previous calculations from the spherulite growth rate and from the overall kinetic rate constant showed that the number of nuclei per unit volume was similar for samples crystallized at equal undercoolings. Had we used a constant value of T, there would have... 

Halides.—The kinetics of crystallization of vitreous Bep2 have been studied, using X-ray diffraction and calorimetric methods. An analysis of the data shows that the crystallization proceeds via spherulitic growth, with an activation energy of 222 kJ mor. The enthalpy increments of Bep2 have been measured by the drop method, in both the glassy and liquid states, from 450 to 914 K. ... 

The influence of PMMA content on the kinetic and thermodynamic parameters controlling the isothermal spherulitic growth and the overall crystallization rate of PEG from the molten blends has been analyzed on the basis of the modified Tumbul 1-Fisher equation ... 

Thus, the value of t which the //, intensity is a maximum serves as a measure of R and may be used to follow the spherulite growth. An automatic device has been described for scanning the pattern for rapidly following the growth kinet cs. ... 

Direct observation of spherulite growth rates during isothermal crystallization yields fundamental information about the kinetics of this process because the results can be compared with pertinent theories and basic parameters can be quantified. However, such experiments are tedious and only a few studies on blends have been reported. Of related interest are a number of reports on the crystallization of blends of fractions of the same polymer but of differing molecular weights. This approach is useful for assessing the role of overall chain mobility and has shown in some instances that molecular weight segregation occurs on crystallization (20). 

In this kinetic view, the small scale interlamellar segregation seen for i-PS/PPO and PCL/PVC blends is believed to be the result of the higher Tg of the amorphous component compared to the crystallizable one which causes diffusion to dominate whereas, in the i-PS/a-PS system the decreased spherulite growth rate is believed to cause... 

As mentioned above, PLA should be addressed as a random copolymer rather than as a homopolymer the properties of the former depend on the ratio between L-lactic acid and D-lactic acid units. A few studies describe the influence of the concentration of D-lactic acid co-units in the PLLA macromolecule on the crystallization kinetics [15, 37, 77-79]. The incorporation of D-lactic acid co-units reduces the radial growth rate of spherulites and increases the induction period of spherulite formation, as is typical for random copolymers. In a recent work, the influence of the chain structure on the crystal polymorphism of PL A was detailed [15], with the results summarized in Figure 5.13. It shows the influence of D-lactic acid units on spherulite growth rates and crystal polymorphism of PLA for two selected molar mass ranges. 

The average values n are indicative of thermal and/or athermal nucleation followed by a three-dimensional crystal growth. Indeed, for spherulitic growth and athermal nucleation, n is expected to be 3. In the case of thermal nucleation, it is expected to be 4 [2], However, complications in the Avrami analysis often arise because several assumptions, not completely applicable to polymer crystallization, are involved in the derivation. A comparison of some crystallization kinetics parameters is summarized in Table 3.5 [70-80]. 

In the following part, a discussion on the crystallization behavior in immiscible polymer blends is given, including the nucleation behavior, spherulite growth, overall crystallization kinetics, and final semicrystalline morphology. Each topic is illustrated with several examples from the literature to allow the reader to find enough references on the discussed subject for further information. 

Recently the statistical approach was developed [5] for the description of the kinetics of conversion of melt to spherulites and the kinetics of formation of spherulitic pattern during both isothermal and nonisothermal crystallizations. The final spherulitic pattern can also be described. The rates of formation of spherulitic interiors and boundaries (boundary lines, surfaces and points) as well as the their final amounts could be predicted if spherulite growth and nucleation rates are known. Applied to iPP crystallized during cooling with various rates, the approach allowed for the predictions of tendencies in the kinetics of formation of spherulitic structure and its final form. 

The radial growth kinetics of PHB spherulite formation have been evaluated in terms of Hoffman s theoretical relationship ... 

To determine the parameters Go and Kg, one needs to measure the growth rate G(7). For materials with slow crystallization kinetics, one can easily measure the spherulite growth rate as a function of temperature from micrographs (Fig. 4.2). Then Gq and Kg are determined by plotting In G + W/Rg T - T ) against T + T ) jlT AT. 

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